Mr. J. H. Alexander on the Tension of Vapour of Water. 107 



ations are given in Centigrade degrees, and belong to the same 

 side of the equation with the temperatures given by the re- 

 spective formulse. 



FormuliB proposed by 

 Tredgold.i Roche. ] Coriolis. I Dulong. J. H. A, 



0-69 I 0-63 080 



Maximum deviation in excess 



MaxiiBum deviation in defect 2-11 [ 075 



Mean deviation without regard to signs: 0-79 0'37 

 Mean deviation with regard to signs... l4-0'338 —0001 



0-25 



0-40 

 073 



0-44 i 0-24 

 -0-363! -0 007 



flO 



1-20 



0-60 



-0-20 



The last formula, as is seen, although the sum of its devia- 

 tions is greater than two or three of the others, lies yet more 

 symmetrically with the curve of the experiments than any. 



The three first are given by M. Dulong, after a copious 

 enumeration of different formulae, as agreeing the best with 

 observation. Of these, in that of Tredgold and of Coriolis, 

 the elasticity is a function of the temperature; but M. Coriolis 

 uses, instead of an integral, a mixed fractional index. His 

 exponent, instead of 7 as Dr. Young took, or 6 as Creighton 

 and Tredgold preferred, or 5*13 as Southern chose, or 5 as 

 Dulong adopted, is 5'335 ; whose coincidence with the natural 

 law is only empirical, and can be but accidental. In the for- 

 mula of M. Roche (which he offers, not as a means of inter- 

 polation, but as the expression of a general physical law), the 

 temperature is itself an element of the index by which certain 

 constant quantities are to be involved. The principles, how- 

 ever, upon which he has founded the expression, are disap- 

 proved both by M. Dulong and M. Regnault. The formula 

 of M. Dulong presents a smaller aggregate deviation than any 

 of the others ; and it would be singular if it did not, seeing 

 that it was derived from a constant furnished by his own ex- 

 periments. But as might also be anticipated, this constant, 

 taken (to four places of' decimals) from the result of thehigh- 

 .est experimental temperature, fails to apply in the lower ones. 

 The maximum deviation under his formula, given in the last 

 table, occurs at the lowest experimental temperature ; and in 

 fact in his final table of atmospheric pressures and correspond- 

 ing temperatures, he has preferred, below the limit of four 

 atmospheres (l4.5°-4 C. or 293°'72 F.), to abandon his own 

 formula and use that of Tredgold. Below the ordinary atmo- 

 spheric pressure his quantities are utterly inapplicable, as will 

 be seen by the following statement: — ' 



